Continuous record Laplace-based inference about the break date in structural change models
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Citation (published version)Alessandro Casini, Pierre Perron. 2018. "Continuous Record Laplace-based Inference about the Break Date in Structural Change Models."
Building upon the continuous record asymptotic framework recently introduced by Casiniand Perron (2017a) for inference in structural change models, we propose a Laplace-based(Quasi-Bayes) procedure for the construction of the estimate and confidence set for the dateof a structural change. The procedure relies on a Laplace-type estimator defined by anintegration-based rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to asthe Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is definedas the minimizer of the expected risk with the expectation taken under the Quasi-posterior.Besides providing an alternative estimate that is more precise—lower mean absolute error(MAE) and lower root-mean squared error (RMSE)—than the usual least-squares one, theQuasi-posterior distribution can be used to construct asymptotically valid inference usingthe concept of Highest Density Region. The resulting Laplace-based inferential procedureproposed is shown to have lower MAE and RMSE, and the confidence sets strike the bestbalance between empirical coverage rates and average lengths of the confidence sets relativeto traditional long-span methods, whether the break size is small or large.